We are going to investigate the feasibility of treating atoms as harmonic oscillators, even if their potential wells are not parabolic. Consider a particle in one dimension that has potential energy V(x) = -V0.
(a) What is the equilibrium position of the particle? (I.e., where is V(x) a minimum?)
(b) Write out the Taylor series expansion for V(x) about the equilibrium position, keeping only the zeroth, first, and second order terms in x. (Note that this makes it a harmonic oscillator.)
(c) By what percentage does this expansion differ from the real value of V(x) at x = 0.1? At x = 0.5?